Hoffman, Frederick

The subject of this thesis is the design and
implement at ion of an expert system from a standard data
base management software language. The advantages and
limitations of such a system design are discussed and
supported by an accompanying implementation. Both, the
design and implementation, demonstrate what gives the
expertise or personification of human reasoning to a
machine and why this type of reasoning is well suited to
certain types of problems. This fundamental departure from
traditional deterministic analytical problem solving is
accomplished by developing a system that is heuristic in
nature. This heuristic implementation provides for a
system that assists in the development of an emerging
solution, rather than a deterministic solution in and of
itself (i.e., a system that is programmed with a set of
meta-knowledge rules that governs the decision making
process and acts upon a second set of knowledge rules).

Recent interest in cryptographic systems has generated many mathematical results involving computations in finite fields. In particular, it is known that the use of optimal normal bases significantly reduces the complexity of computations in certain finite fields. This thesis examines three specific aspects of optimal normal bases. First, the effect of optimal normal bases on computations in finite fields is analyzed. Second, the known constructions of optimal normal bases are presented. Finally, the generators of optimal normal bases are discussed in terms of their order in the field.

This thesis examines IDC--the Interim Data Collector, a program developed to store diverse technical data in the domain of avionics. The program generates a dialogue through menus and allows rapid data entry and retrieval based on operator supplied information about the modules. The program is written in CLIPPER (a superset of DBASE III+). I will show that IDC exhibits the characteristics associated with programs known as expert systems. These include data directed search, hierarchical dynamic pruning, an interactive user interface and a blackboard type inference engine. I also discuss the various sources of faults which contribute to reliability problems during program use and examine several techniques to increase the reliability of the expert system.

The intent of this thesis is to show how rule structures can be derived from influence diagrams and how these structures can be mapped to existing rule-based shell paradigms. We shall demonstrate this mapping with an existing shell having the Evidence (E) --> Hypothesis (H), Certainty Factor (CF) paradigm structure. Influence diagrams are graphical representations of hypothesis to evidence, directed forms of Bayesian influence networks. These allow for inferencing about both diagnostic and predictive (or causal) behavior based on uncertain evidence. We show how this can be implemented through a Probability (P) to CF mapping algorithm and a rule-set conflict resolution methodology. The thesis contains a discussion about the application of probabilistic semantics from Bayesian networks and of decision theory, to derive qualitative assertions about the likelihood of an occurrence; the sensitivity of a conclusion; and other indicators of usefulness. We show an example of this type of capability by the addition of a probability range function for the premise clause in our shell's rule structure.

The costs associated with the design and manufacture of machined components can be significantly reduced by the ability to identify and group similar parts. This activity is generally accomplished by assigning each part a Group Technology code number based on its most significant characteristics. Attempts to accomplish this are hindered by: the relatively small amount of information that can be encoded in a code of manageable length, inconsistencies in human interpretation of design and manufacturing data, the commitment of resources required to review and encode all candidate components at a facility, and the heuristic nature of determining what constitutes significant similarity for any particular application. These problems are addressed by the development of a system that assists in the determination of similarity by comparing CAD (Computer Aided Design) files, rather than Group Technology codes, in a manufacturing oriented frame-based system.

This paper describes an Automated Software Development Methodology (ASDM)
that encompasses a formal model for characterizing the specifications of a system
that will ultimately manifest itself in a software system. This paper focuses on the
semantic specification model of ASDM and the architecture of a knowledge-based
expert system (KBES) supporting the semantic model. ASDM is a
knowledge-based expert system, because it provides expertise and assistance m
the construction of formal requirement and design specifications while hiding the
formal specification techniques and semantic model from the user. ASDM is a
knowledge-based system, because the system represents formally characterized
knowledge of the ASDM semantic model, and it represents application domain
specific knowledge of a problem domain. Lastly, this paper introduces the
concept of an Application Domain Communication Model (ADCM), with its
associated characterization and interpretation facilities, for defining a set of user
interface scenarios that represent a cognitive model of an application domain
engineering world.

A study was made of the problem of locating M facilities
on a connected grid graph, so that M is the minimum and so
that every demand node on the graph is within given distance
K of one of these M facilities. We call this problem briefly
the G(N,K,M) problem, with N denoting the total number
of demand nodes. An algorithm for solving this problem by using backtrack
technique is presented in this thesis. A heuristic algorithm
is also present; although the resulting M is not always minimum,
it tends to be near minimum. The advantage over the
backtrack algorithm is that the heuristic algorithm operates
very quickly. Algorithms represented in this thesis are programmed in
the Pascal language for the Univac 1100 computer at Florida
Atlantic University, Boca Raton, Florida.

Properties of Goppa codes are studied. These are
"good" codes in the sense that they asymptotically
approach the Varshamov-Gilbert bound. E. N. Gilbert and
R. R. Varshamov have shown (independently) that it is
possible to construct an (n, k) linear code over GF(q)
with minimum distance d if [equation] and there are long Goppa codes which achieve this bound [10]. Subclasses of Goppa codes which remain invariant under symmetries are given special attention.

In this thesis we give a self-contained exposition
of the group-theoretic proofs of the Burnside p^a g^b theorem. The Burnside p^a g^b theorem states that all
groups of order p^a g^b are solvable, where p and q are primes. The proof was suggested by Thompson,
and published by Goldschmidt, Bender, and Matsuyama.

In this paper, we assume a proper pairwise balanced design on 30 points exists. We then get some results that reveal what the largest line size may be and the maximum number of lines of this size. Using these results, we look at one of two cases. We investigate the structure of the linear spaces in this case having no lines of sizes 2, 3, 6 and 30 and rule out many possibilities in order to get a minimum number of possible solutions.